Artificial intelligence guided research and development

ABSTRACT

Recommendations for new experiments are generated via a pipeline that includes a predictive model and a preference procedure. In one example, a definition of a development task includes experiment parameters that may be varied, the outcomes of interest and the desired goals or specifications. Existing experimental data is used by machine learning algorithms to train a predictive model. The software system generates candidate experiments and uses the trained predictive model to predict the outcomes of the candidate experiments based on their parameters. A merit function (referred to as a preference function) is calculated for the candidate experiments. The preference function is a function of the experiment parameters and/or the predicted outcomes. It may also be a function of features that are derived from these quantities. The candidate experiments are ranked based on the preference function.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Patent Application Ser. No. 62/547,723, “ArtificialIntelligence Guided Research and Development,” filed Aug. 18, 2018. Thesubject matter of all of the foregoing is incorporated herein byreference in their entirety.

BACKGROUND 1. Technical Field

This disclosure relates generally to artificial intelligence used torecommend experiments, for example for materials or process development.

2. Description of the Related Art

Industrial research and development teams are often tasked withdeveloping a new material or process that meets a specific set ofspecifications or goals. An experimenter will run experiments that trydifferent combinations of process parameters and compositions ofingredients. The experimenter will choose a set of experiments based onhis experience, intuition, and research with the hope that the resultsof the experiments will meet the goals. To guide his choice ofexperiments, an experimenter may rely on design of experiments methodsthat set up a series of experiments to be tested that systematically trya variety of combinations of the experimental parameters of interest.

Oftentimes, the lists of goals and adjustable experimental parametersare long and diverse, and it may not be clear how to incorporate orprioritize all the different combinations to be tried. Traditionaldesign of experiments techniques often assume linear relationshipsbetween inputs and set up orthogonal arrays of experiments that will notdiscover intricate, non-linear interactions between input parameters.Moreover, these techniques insufficiently handle high-dimensionalproblems with many experimental parameters. Experimenters often runsequences of experiments with many of the experimental parameters heldfixed based on their own guesses for which parameters will matter most.This approach eschews statistical modeling in favor of experimenterintuition and results in a haphazardly selected set of experiments thatmay not adequately test enough variations of parameters.

Thus, there is a need for a better approach to the design ofexperiments.

SUMMARY

The present invention overcomes the limitations of the prior art bygenerating recommendations for new experiments via a pipeline thatincludes a predictive model and a preference procedure.

Other aspects include components, devices, systems, improvements,methods, processes, applications, computer readable mediums, and othertechnologies related to any of the above.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure have other advantages and features whichwill be more readily apparent from the following detailed descriptionand the appended claims, when taken in conjunction with the examples inthe accompanying drawings, in which:

FIG. 1 is a flow diagram of a development testing loop according to anembodiment.

FIG. 2 is a screenshot of an example form for an experimenter to enterexperiment goals and priorities.

FIG. 3 is a screenshot of an example form for an experimenter to enterexperiment parameters and constraints.

FIG. 4 is a flow diagram of an artificial intelligence-guided experimentgeneration process.

FIG. 5 is a screenshot of a user interface for predictions to translatebetween testing conditions.

FIG. 6 is a screenshot of a user interface to analyze correlations in adata set.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The figures and the following description relate to preferredembodiments by way of illustration only. It should be noted that fromthe following discussion, alternative embodiments of the structures andmethods disclosed herein will be readily recognized as viablealternatives that may be employed without departing from the principlesof what is claimed.

A preferred embodiment includes a multi-component software system withwhich an experimenter interacts. FIG. 1 outlines the steps of oneexample of a development testing process that a development team mightuse. Information about the development task is entered 110. This mayinclude a definition of the development task, such as the experimentparameters that may be varied, the outcome variables and the desiredgoals or specifications. Existing experimental data is also entered 120into the software system. The software system uses machine learningalgorithms to train 130 a predictive model using that data. The softwaresystem generates 140 candidate experiments and uses the trainedpredictive model to predict 150 the outcomes of the candidateexperiments based on their parameters. A merit function (referred to asa preference function) is calculated 160 for the candidate experiments.The preference function is a function of the experiment parametersand/or the predicted outcomes. It may also be a function of featuresthat are derived from these quantities. The candidate experiments areranked 170 based on the preference function. The experimenter runs 180the experiments from the recommendation list. Optionally, the outcomes190 may be reported back to the software system for further training130.

In the preferred embodiment, the experimenter submits information aboutthe development task into a web platform. In an alternative embodiment,similar information may be collected in a spreadsheet and emailed.

FIG. 2 is a screenshot of one example of a user interface form to submitinformation about the goals for the development task. The experimenteradds various goals to create rows in the interface. In this example, thegoals are for measurements that are made after an experiment is run. Theexperimenter can select a priority 210 for each goal. Here, the choicesfor priorities are “High,” “Medium,” “Low,” and “Ignore.” The “Ignore”option allows the goal to be ignored when generating experiments. Theother three options provide a simple scale from which the experimentercan choose. An alternative embodiment might have a numerical value forpriority that provides more complex choices.

In the next column, the experimenter can specify the goal type 220.Possible options that might be included here include the following.“Maximize” means the goal is to maximize the outcome. “Minimize” meansthe goal is to minimize the outcome. “Range” means the goal is to fallwithin a specified range. “Target” means the goal is to be as close aspossible to a particular target.

The “Threshold” value 230 is the requirement. The outcome must meet thisvalue in order to meet the specification. The experimenter may alsoprovide an additional optimistic “Goal” 240 that provides someindication of the scale of the measurement. One way to think of thescale is the difference between the required threshold 230 and anoptimistic goal 240. An alternative embodiment might ask for a scaledirectly. The scale is important to be able to prioritize changes indifferent outcomes. For example, it may provide a way to compare achange of one dollar in price with a change of one degree in meltingtemperature. In another possible embodiment, the scientist may work witha third-party data scientist to communicate the information, and thenthe data scientist may fill out the same information in a spreadsheet.

FIG. 3 is a screenshot of an example form for an experimenter to enterexperiment parameters and constraints. This example is for experimentsto optimize a material formulation and/or material processing. FIG. 3shows three sections. The first section lists the “FormulationIngredients” 310. This form collects information on ingredients that maybe included in a material development task. Ingredients are listed ineach row and grouped by category. In this example, for each ingredient,the experimenter provides a minimum and maximum amount 320 that can beused in a formulation. Here, these quantities may represent either partsper hundred of the quantity of one of the categories or weightpercentages.

The second section in FIG. 3 is for entry of information about processparameters and other stand-alone parameters that are not ingredients ina formulation 330. For every parameter defined in the first twosections, the experimenter may elect to merge that parameter withanother via the “Treat As” selection 340 or ignore it for the purposesof modeling and generation. This “Treat As” option helps to reduce thedimensionality of the experiment parameters that may be varied. Duringthe recommendation process, a parameter that is “Treated As” anotherparameter may be removed from the vectorized representation of the data.The quantity that used to represent that merged parameter may be addedto the parameter it is being treated as. That way, the data for thatparameter is still contributing but the dimension of the vector used forrepresenting an experiment is smaller.

The third section in FIG. 3 allows an experimenter to specifyconstraints 350 on the experiment parameters. For example, theexperimenter might require that a parameter always be used in anexperiment, that the ratio between two parameters be constrained, thattwo or more parameters never be used together, that two or moreparameters always be used together, or that an arbitrary function of theparameter values be less than or equal to some value. Additionally, notpictured in FIG. 3 is the option for an experimenter to add propertiesto each parameter. These properties could include the cost of using aparameter, the physical properties such as specific gravity or viscosityof a parameter, or other arbitrary values. It is preferred that theseproperties be consistent across categories for modeling purposes. Inanother possible embodiment, the scientist may work with a third-partydata scientist to communicate the information, and then the datascientist may fill out the same information in a spreadsheet.

In some embodiments, the experimenter also submits data from previousexperiments into a web platform. In an alternative embodiment, theexperimenter may send past data via email or another form of electroniccommunication. The data from those previous experiments (i.e.,parameters for the previous experiments and their correspondingoutcomes) can now be incorporated into the model. Data from previousexperiments is not necessary; however, if there are no previous results,there is nothing to model and candidate experiments may bepseudo-randomly chosen within the constrained experimental space.

In one example of a predictive model, the model takes as input a vectorof numbers describing an experiment and produces a vector of predictedoutcomes. The vectorized description of an experiment may include both adirect encoding of the parameters of the experiments as well as a set ofadditional derived features. Including derived features provides moredata from which the model can learn. Derived features may includenumbers used to compute constraints such as ratios or additionalproperties such as the total specific gravity or cost of a formulation.Derived features may also include totals across categories, univariatetransformations of parameters such as power transforms, multivariatetransformations such as parameter products or sums, or other arbitraryfunctions of the parameters. The derived features may also be based onthe outcomes in addition to the experiment parameters.

In one approach, individual machine learning models are used to predicteach outcome separately, but an alternative embodiment might have asingle statistical or machine learning model. In some cases, a Gaussianprocess regression model is used to predict each outcome. The kernel ofthe Gaussian process may be computed as follows:k(x _(i) ,x _(j))=σ₀δ_(i,j)+σ₁ k′(√{square root over (Σ_(l) w _(l)(x_(i) _(l) −x _(j) _(l) )²)})  (1)where x_(i) and x_(j) are two experiment vectors, σ₀ is a parameter forrandom experimental noise and allows for matrix invertibility, δ is thekronecker delta, σ₁ is a parameter for the variance explained by thestationary kernel, k′ is a chosen stationary kernel function, and w is avector of weights with the same number of dimensions as the experimentvectors. In practice, Matern 3/2 covariance functions work well for k′.The parameter w equips k with automatic relevance determination thatprovides built-in feature selection.

Model training is the process of determining the best values for themodel parameters including those that are intrinsic to the stationarykernel. Training may be conducted separately for each model with anoptimization procedure applied to the predictive error of the model. Oneadvantage of training separate Gaussian process models is that eachprediction comes with an estimate of the standard deviation. Whenselecting experiments, this standard deviation may be used to create anactive learning policy that helps to ensure a variety of experiments.The standard deviation may be used to create an upper confidence bound.Alternative embodiments might use expected improvement or othersolutions in the stochastic multi-armed bandit problem literature. In analternative embodiment, one might choose to use a different type ofmodel such as neural networks, decision trees, kernel ridge regressions,linear regressions, or an ensemble of many models.

FIG. 4 is a flow diagram of one implementation of steps 140-170 ofFIG. 1. Thousands of candidate experiments are randomly generated.Predictions of their outcomes are made. The predicted outcomes arecombined via a preference function into a single score. The candidatesare ranked and the ones with the highest score may be chosen for actualimplementation. Each step is explained in detail below.

A pseudo-random sampler 401 is employed to generate sample experiments.An alternative embodiment might use a different search procedure tocover the allowed experiment space. One version uses a scrambled Haltonsequence as the sampler because of its digital net properties. Thesampler returns vectors in the unit hyper-cube. Those vectors aretransformed using the minimum and maximum constraints provided to have ahigher chance of falling within the problem constraints. Some dimensionsof the vector may be set to zero randomly if sparsity in the parametersis required.

The sample experiments 402 may be processed one at a time or in batchesdepending on the dimensionality of the problem. Randomly generatedsamples may not meet the constraints of the problem. For example, theproblem might require that the weight percentages of a formulation addup to 100. In FIG. 4, a normalizing process 403 is used to increase thesuccess rate of the rejection sampling procedure. This normalizingprocess performs quick operations to ensures additional constraints aremet. Alternative embodiments might skip this step and instead accept ahigher rejection rate. Sample experiments are checked 404 againstconstraints including the ones that were entered into the web platformor communicated by the experimenter. Candidates that do not meet theconstraints are thrown out. The remaining candidates are considered tobe valid candidates 405 for experimentation.

Derived features can then be computed 406 for the remaining candidates.The derived features are concatenated together to produce a featurevector 407. These features are checked 408 against any constraints onthe features. Typical constraints might include limiting the cost of aset of parameters, limiting the total amount of a category, and limitingthe total number of non-zero parameters in a category. Passingcandidates are encoded 409 in vectors to be fed into the model. Themodel predicts 410 a vector of outcomes.

To compare proposed experiments, a preference function is created thatincorporates the data for an experiment and its predicted properties.This function takes as input the experimental parameters, the derivedfeatures, and the predicted outcomes and outputs a single score. In oneapproach, the preference function is additive, borrowing from additiveutility functions in economic theory. Each additive component isweighted according to the priority of the goal and is shaped accordingto the goal quantity and type. For example, the additive components maybe negative exponentials and transformed such that they equal ten timesa priority weight when the outcome is at the threshold and zero at thegoal. This multiplicative transformation allows the preference functionto be dimensionless and not dependent on units of measure. Two differentadditive components may be used for range and target goal types tocreate a bowl-like shape around the goal region. In alternativeembodiments, different preference functions may be used such as squarederror to a set of goals, linear additive utilities, quadratic additiveutilities, or logarithmic additive utilities. The experiment parametervector, feature vector, and outcome vector are fed into the preferencefunction 411 resulting in a preference score 412 for the candidateexperiment. This preference function provides a method for ranking pastand candidate experiments according to their desirability to theexperimenter. The inclusion of derived features as a parameter to thisfunction allows for cost and other properties to be a consideration forthat ranking.

Experimental variability and model uncertainty can be incorporated intothe preference function by using a Monte Carlo procedure to sample overmany different outcome conditions using the distributional estimatesfrom a Gaussian process or another machine learning model. Thepreference function is applied to each sampled outcome to get adistribution of preference function values. To collapse the distributioninto a single value, one may simply consider the average, or apply anactive learning procedure to extract, for example, a percentile of thatpreference distribution or an expected value of a portion of it. Thesecollapsed values can then be used as the preference values for thepurpose of comparison.

Once a preference function value is computed for the candidateexperiment, it can be stored 413 in a list of other candidates. Tofurther optimize the candidate, a local optimization procedure 414 canbe run to make slight adjustments. Back propagation may be used tocompute the derivative of the preference function with respect to thecandidate experiment and then use a gradient descent procedure to makeadjustments. The adjusted experiment can be sent back through the entirepipeline starting with the normalization step. This whole samplingprocess is repeated thousands of times to develop a list of candidateexperiments. The candidate experiments with the smallest preferencescore are returned to the experimenter. In order to ensure that theexperiments vary appropriately, a batch of experiments may beconstructed one-by-one each time re-computing the upper confidence boundpreference score after including a lower confidence bound prediction ofpreviously chosen experiments as data in the predictive model.

The experimenter run the selected experiments and reports back theresults. In one implementation, the system performed well after onlythree iterations of testing. Each iteration usually involved testingbetween eight and twenty experiments.

The software system may make various interfaces available to theexperimenter for the experimenter to conduct his or her own analysis.One possible interface is one that allows an experimenter to predict howa test result under one testing condition will translate to a resultunder a different testing condition. FIG. 5 shows an example. In thisinterface, the experimenter selects the type of experiment 510 that isbeing run. The experimenter can select the original conditions 520 forthe experiment, including properties like the substrate the experimentwas conducted on, how long the material was aged for and at whattemperature. The experimenter can select the same parameters 530 for theconditions for which he or she desires a prediction. The experimenteralso enters the outcome 540 under the original condition—the fieldlabeled “Original Quantity” in the preferred embodiment. The interfacewill then display in either text or graphical format a prediction 550for the range of values under that new experimenting condition. A plotmay also be displayed showing the prediction function with the originalquantity on the x-axis and the predicted quantity on the y-axis. In someimplementations, the predictions are made using a machine learning modelsuch as a linear regression or a Gaussian process.

Another interface may allow an experimenter to view correlations acrossinputs (experiment parameters) and outputs (outcomes) in the experimentdata set. FIG. 6 shows a screenshot of an example. Experiment parameters610 are listed on the left, and outcomes 620 are listed on the right.They are connected in a Sankey diagram where connections 630 representpositive correlations and connections 640 represent negativecorrelations. The polarity (positive or negative correlation) may berepresented by different colors. The width of each connection isproportional to the absolute value of the Pearson correlation betweenthe parameter and the outcome across the dataset. In this example, onlycorrelations above both a threshold of 0.5 and with a p-value of lessthan 0.005 according to a statistical hypothesis test are displayed. Inan alternative embodiment, different cutoffs might be employed to showmore or fewer correlations. The experimenter may select inputs andoutputs at the top 650 of the interface to ensure that only those inputsand outputs are shown, enter in a number for the minimum number 660 ofsamples for a correlation to be displayed, and add filters 670 so thatthe correlations are calculated only on data points that meet variouscriteria. Clicking on one of the Sankey diagram connections brings theexperimenter to a scatter plot with the parameter on the x-axis and theoutcome on the y-axis. In an alternative embodiment, an interface mayalso allow an experimenter to view correlations between differentparameters or between different outcomes as well.

Additional interfaces may be included in the software. Examples includean interface that allows users to see scatter plots for multipleparameters and outcomes, an interface that shows formulationsside-by-side in a spreadsheet style view, and an interface that allowsthe user to query for particular sets of formulations by parameter andoutcome values. By having the experimental data in this software, entireteams of scientists can collaborate using the same data. Multiplescientists can use the software at the same time from different webbrowsers.

The software allows for detailed information to be entered about eachexperiment. In some embodiments, a user may be allowed to enter amaterial lot that an ingredient came from when running that particularexperiment. A material lot may have metadata data associated with itincluding, for instance, its date of purchase, specifications providedby the supplier, and freeform notes. A user may also add notes to anexperiment or additional process parameters to associate structuredmetadata with the experiment, such as which machine the experiment ranon, what date the experiment was run, or what operator ran theexperiment. A user may enter multiple measurements for each outcome. Inthe preferred embodiment, the software automatically computes the meanand standard deviation for each set of measurements.

An example application is for a rubber development process. The goal ofthe process may be to match a specification sheet that lists a varietyof properties. Past data may include experiments that were run in thepast for a similar application. Ingredients may include a set ofpolymers, oils, carbon black fillers, silica fillers, processing aids,curatives, and other additives. The parameter vectors for the model,each of which represents a formulation, may be set up as a list ofweight percentages or parts per hundred parts polymer of each ingredientwith zeros when an ingredient is not present. Process parameters such ascure time, cure temperature, and number of mixing passes may be appendedto the vector. Derived features might include the total amount offiller, the ratio of filler to processing aids, the weighted averagemolecular weights of the polymers, the raw material cost of thecompound, the cost of the compound at the predicted density, and thecount of the number of polymers included. Possible measurements thatwill be predicted by the predictive model and incorporated into thepreference function may include rheology data, cure rate, elongation,tensile strength, and elastic modulus. The preference function may beconstructed so that it achieves a value of zero if and only if all themeasurements satisfy the required specifications.

A special case of the rubber development process is the development ofrubber compounds for tires. For tire development, ingredients mayinclude may different types of rubber compounds such as natural andsynthetic rubber as well as other ingredients like fillers, processingaids, and curatives. Outcomes could include measuring the tread of thetire, the degree of wear on the tire, and the grip of the tire indifferent environmental conditions.

Another example use could involve optimizing process parameters on afactory line that produces parts or during a chemical productionprocess. The goal may be to reduce defects, increase throughput, and/orincrease part quality. Past data may include defect and scrap counts forthe line run at different speeds. Process parameters may include linespeed, temperatures of various stages of the line, and physical andchemical properties and dimensions of parts or batches on the line. Theparameter vector may directly list the various process parameters thatcan be changed. The outcomes to be predicted may include scrap anddefect percentages. Different types of defects may be considered asdifferent outcomes. The preference function may be constructed so thatit trades off throughput with defect rates.

Another example use case is for experimentation for drug development. Inone potential embodiment, the experiments might be recommended foroptimizing drug delivery and stability. Potential types of drug deliveryand stability use cases could include drugs that are administered viainjection such as intravenous, intramuscular, or subcutaneous injectionsor orally with a pill. In each case, potential parameters include theformulation for the fluid or substance used as a vehicle for the activeingredient to be delivered as well as parameters that describe thephysical mechanism of delivery. Special attention might be placed on thebiochemical properties of the ingredients included. Derived featurescould include the pKa of each ingredient and molecular weight and otherstoichiometric considerations. Potential outcomes could include theviscosity, pH, concentrations of various ions, stability in differenttemperature conditions, resulting concentration of the activeingredient, and pain caused by administration of the drug. The goalmight be for some of the properties to be as close to the body'shomeostasis levels to prevent side effects. An alternative applicationto drug development could include focus on the manufacturing process toscale up production of a drug. This application would entail optimizingwith various process parameters as parameters and product yields, defectrates, and throughputs as outcomes.

A further example use case is for experimentation for consumer productdevelopment. Consumer products could include health products likesunscreen, consumable products like food and beverages, and cosmeticslike lipstick or perfume. For consumer products, there might be verytight cost constraints or a desire for the preference function to put alot of weight on cost as a feature derived for the formulation of theproduct. Experiments for consumer products could include testing newformulations and compositions or new production processes formanufacturing. Consumer products may have constraints based on thedesire to market a product a certain way—they may need to include acertain percentage of some ingredient to qualify as a particular type ofproduct for legal or marketing reasons such as “fat-free” or“all-natural.” The outcomes for consumer products might includepredictions for consumer preferences. Lab measurements made in a labcould be used as a proxy for consumer preferences. Using past consumerpreference studies, one could statistically determine a relationshipusing a regression or some other means between consumer preferences andlab measurements. Then the predicted consumer preferences could beincluded in the preference function for the candidate experiments ratherthan the lab measurements directly. By incorporating the consumerpreferences, experiments may be recommended to optimize for futuremarket performance rather than concrete scientific metrics.

In some embodiments, experiments may be run in a high-throughput manner.In these cases, experiments are run quickly in large batches and may beautomated. In a possible embodiment, a high-throughput experiment systemmight communicate electronically with software that can recommendexperiments automatically as the high-throughput system completes eachrun.

As an additional example, the experiments could be for the developmentof new paint or color matching. For paint, outcomes could include theviscosity of the paint, the application feel, and the color. Forpurposes of predictions for the color of the paint or color matching inother contexts, color might be represented as LAB values or RGB valuesor both. The preference function might either incorporate those valuesdirectly or be set to use a delta E calculation which provides a singlenumber to describe differences between colors. Other properties of thecolor of the paint might be used such as measured color under differentilluminations or angles or the metamerism of the paint. The experimentparameters might be the quantity of ingredients added to the paintincluding possibly a base component, color additives, and processingaids.

Although the detailed description contains many specifics, these shouldnot be construed as limiting the scope of the invention but merely asillustrating different examples. It should be appreciated that the scopeof the disclosure includes other embodiments not discussed in detailabove. For example, other embodiments may use alternative machinelearning models, sampling algorithms, and active learning procedures.Various other modifications, changes and variations which will beapparent to those skilled in the art may be made in the arrangement,operation and details of the method and apparatus disclosed hereinwithout departing from the spirit and scope as defined in the appendedclaims. Therefore, the scope of the invention should be determined bythe appended claims and their legal equivalents.

Alternative embodiments are implemented in modules in computer hardware,firmware, software, and/or combinations thereof. Implementations can beimplemented in a computer program product tangibly embodied in acomputer-readable storage device for execution by a programmableprocessor; and method steps can be performed by a programmable processorexecuting a program of instructions to perform functions by operating oninput data and generating output. Embodiments can be implementedadvantageously in one or more computer programs that are executable on aprogrammable computer system including at least one programmableprocessor coupled to receive data and instructions from, and to transmitdata and instructions to, a data storage system, at least one inputdevice, and at least one output device. Each computer program can beimplemented in a high-level procedural or object-oriented programminglanguage, or in assembly or machine language if desired; and in anycase, the language can be a compiled or interpreted language. Suitableprocessors include, by way of example, both general and special purposemicroprocessors. Generally, a processor will receive instructions anddata from a read-only memory and/or a random-access memory. Generally, acomputer will include one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, andFlash-memory devices; magnetic disks such as internal hard disks andremovable disks; magneto-optical disks; and CD-ROM disks. Any of theforegoing can be supplemented by, or incorporated in, ASICs(application-specific integrated circuits), FPGAs and other forms ofhardware.

What is claimed is:
 1. A method implemented on a computer systemcomprising a processor, the processor executing instructions to effect amethod for recommending candidate experiments, the method comprisingtraining a predictive model that predicts outcomes of experiments,wherein the training is based on known outcomes of previous experimentscharacterized by known parameters; generating a number of candidateexperiments; using the predictive model to predict outcomes of thecandidate experiments based on parameters of the candidate experiments;and recommending from among the candidate experiments based at least inpart on the predicted outcomes.
 2. The method of claim 1 furthercomprising: running at least one of the recommended experiments; andfurther training the predictive model based on the outcomes of therecommended experiments.
 3. The method of claim 1 wherein recommendingfrom among the candidate experiments comprises: calculating values of apreference function for the candidate experiments, wherein thepreference function is a function of a derived feature that is derivedfrom the parameters and/or predicted outcomes for the candidateexperiments; and ranking the candidate experiments based at least inpart on the calculated values of the preference function.
 4. The methodof claim 3 wherein the derived feature is an estimated cost.
 5. Themethod of claim 3 wherein the preference function is monotonic withrespect to the derived feature but with a slope of increased magnitudebeyond a preselected threshold.
 6. The method of claim 3 wherein thepreference function is a function only of dimensionless variables thatare based on the parameters and/or predicted outcomes for the candidateexperiments.
 7. The method of claim 3 wherein the derived feature is avariability of one of the predicted outcomes.
 8. The method of claim 3wherein the derived feature is a linear combination of the parametersand/or predicted outcomes for the candidate experiments.
 9. The methodof claim 1 wherein the predictive model includes a model of a Gaussianprocess.
 10. The method of claim 9 wherein the predictive model includesa model of a Gaussian process with a Matern kernel and automaticrelevance determination.
 11. The method of claim 1 wherein thepredictive model includes a neural network.
 12. The method of claim 1wherein the predictive model includes an ensemble of models.
 13. Themethod of claim 1 wherein the candidate experiments are generated usinga quasi-Monte Carlo procedure.
 14. The method of claim 1 wherein thecandidate experiments are generated pseudo-randomly, the method furthercomprising: improving the pseudo-randomly generated candidateexperiments using a local optimization procedure.
 15. The method ofclaim 1 wherein the candidate experiments are generated subject toconstraints on a derived feature that is derived from the parametersand/or predicted outcomes for the candidate experiments.
 16. The methodof claim 1 wherein generating the candidate experiments comprises:generating sample experiments; and rejecting those sample experimentsthat do not meet constraints on the parameters for the candidateexperiments.
 17. The method of claim 1 wherein the candidate experimentsare for different formulations of a material or for different processparameters for processing a material.
 18. The method of claim 1 whereinthe candidate experiments are for one of: optimizing rubber properties,optimizing paint, optimizing food, optimizing drug delivery, optimizingdrug stability, optimizing drug production, optimizing production of amaterial, optimizing process parameters for a manufacturing line,optimizing production of a part, optimizing a product for consumerpreferences, or optimizing variations of a product.
 19. A non-transitorycomputer-readable storage medium storing executable computer programinstructions to effect a method for recommending candidate experiments,the instructions executable by a processor and causing the processor toperform a method comprising: training a predictive model that predictsoutcomes of experiments, wherein the training is based on known outcomesof previous experiments characterized by known parameters; generating anumber of candidate experiments; using the predictive model to predictoutcomes of the candidate experiments based on parameters of thecandidate experiments; and recommending from among the candidateexperiments based at least in part on the predicted outcomes.
 20. Asystem for recommending candidate experiments, the system comprising: asource for producing candidate experiments, the candidate experimentscharacterized by parameters; a predictive model that predicts outcomesof the candidate experiments based on the parameters of the candidateexperiments, the predictive model trained on known outcomes of previousexperiments characterized by known parameters; and a module thatrecommends from among the candidate experiments based at least in parton the predicted outcomes.